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Efficient inference in high-dimensional models is a central challenge in machine learning. We introduce the Gaussian Ensemble Belief Propagation (GEnBP) algorithm, which combines the strengths of the Ensemble Kalman Filter (EnKF) and Gaussian Belief Propagation (GaBP) to address this challenge. GEnBP updates ensembles of prior samples into posterior samples by passing low-rank local messages over the edges of a graphical model, enabling efficient handling of high-dimensional states, parameters, and complex, noisy, black-box generation processes. By utilizing local message passing within a graphical model structure, GEnBP effectively manages complex dependency structures and remains computationally efficient even when the ensemble size is much smaller than the inference dimension -- a common scenario in spatiotemporal modeling, image processing, and physical model inversion. We demonstrate that GEnBP can be applied to various problem structures, including data assimilation, system identification, and hierarchical models, and show through experiments that it outperforms existing belief propagation methods in terms of accuracy and computational efficiency. Supporting code is available at https://github.com/danmackinlay/GEnBP, Comment: Under conference submission

While the operationalisation of high-level AI ethics principles into practical AI/ML systems has made progress, there is still a theory-practice gap in managing tensions between the underlying AI ethics aspects. We cover five approaches for addressing the tensions via trade-offs, ranging from rudimentary to complex. The approaches differ in the types of considered context, scope, methods for measuring contexts, and degree of justification. None of the approaches is likely to be appropriate for all organisations, systems, or applications. To address this, we propose a framework which consists of: (i) proactive identification of tensions, (ii) prioritisation and weighting of ethics aspects, (iii) justification and documentation of trade-off decisions. The proposed framework aims to facilitate the implementation of well-rounded AI/ML systems that are appropriate for potential regulatory requirements.

A single unexpected object on the road can cause an accident or may lead to injuries. To prevent this, we need a reliable mechanism for finding anomalous objects on the road. This task, called anomaly segmentation, can be a stepping stone to safe and reliable autonomous driving. Current approaches tackle anomaly segmentation by assigning an anomaly score to each pixel and by grouping anomalous regions using simple heuristics. However, pixel grouping is a limiting factor when it comes to evaluating the segmentation performance of individual anomalous objects. To address the issue of grouping multiple anomaly instances into one, we propose an approach that produces accurate anomaly instance masks. Our approach centers on an out-of-distribution segmentation model for identifying uncertain regions and a strong generalist segmentation model for anomaly instances segmentation. We investigate ways to use uncertain regions to guide such a segmentation model to perform segmentation of anomalous instances. By incorporating strong object priors from a generalist model we additionally improve the per-pixel anomaly segmentation performance. Our approach outperforms current pixel-level anomaly segmentation methods, achieving an AP of 80.08% and 88.98% on the Fishyscapes Lost and Found and the RoadAnomaly validation sets respectively. Project page: https://vision.rwth-aachen.de/ugains, Comment: Accepted for publication at GCPR 2023; Project page at https://vision.rwth-aachen.de/ugains

Classical physical modelling with associated numerical simulation (model-based), and prognostic methods based on the analysis of large amounts of data (data-driven) are the two most common methods used for the mapping of complex physical processes. In recent years, the efficient combination of these approaches has become increasingly important. Continuum mechanics in the core consists of conservation equations that -- in addition to the always necessary specification of the process conditions -- can be supplemented by phenomenological material models. The latter are an idealized image of the specific material behavior that can be determined experimentally, empirically, and based on a wealth of expert knowledge. The more complex the material, the more difficult the calibration is. This situation forms the starting point for this work's hybrid data-driven and model-based approach for mapping a complex physical process in continuum mechanics. Specifically, we use data generated from a classical physical model by the MESHFREE software to train a Principal Component Analysis-based neural network (PCA-NN) for the task of parameter identification of the material model parameters. The obtained results highlight the potential of deep-learning-based hybrid models for determining parameters, which are the key to characterizing materials occurring naturally, and their use in industrial applications (e.g. the interaction of vehicles with sand)., Comment: arXiv admin note: text overlap with arXiv:2212.03130

Wildfire propagation is a highly stochastic process where small changes in environmental conditions (such as wind speed and direction) can lead to large changes in observed behaviour. A traditional approach to quantify uncertainty in fire-front progression is to generate probability maps via ensembles of simulations. However, use of ensembles is typically computationally expensive, which can limit the scope of uncertainty analysis. To address this, we explore the use of a spatio-temporal neural-based modelling approach to directly estimate the likelihood of fire propagation given uncertainty in input parameters. The uncertainty is represented by deliberately perturbing the input weather forecast during model training. The computational load is concentrated in the model training process, which allows larger probability spaces to be explored during deployment. Empirical evaluations indicate that the proposed model achieves comparable fire boundaries to those produced by the traditional SPARK simulation platform, with an overall Jaccard index (similarity score) of 67.4% on a set of 35 simulated fires. When compared to a related neural model (emulator) which was employed to generate probability maps via ensembles of emulated fires, the proposed approach produces competitive Jaccard similarity scores while being approximately an order of magnitude faster.

We present a novel approach of discretizing variable coefficient diffusion operators in the context of meshfree generalized finite difference methods. Our ansatz uses properties of derived operators and combines the discrete Laplace operator with reconstruction functions approximating the diffusion coefficient. Provided that the reconstructions are of a sufficiently high order, we prove that the order of accuracy of the discrete Laplace operator transfers to the derived diffusion operator. We show that the new discrete diffusion operator inherits the diagonal dominance property of the discrete Laplace operator. Finally, we present the possibility of discretizing anisotropic diffusion operators with the help of derived operators. Our numerical results for Poisson's equation and the heat equation show that even low-order reconstructions preserve the order of the underlying discrete Laplace operator for sufficiently smooth diffusion coefficients. In experiments, we demonstrate the applicability of the new discrete diffusion operator to interface problems with point clouds not aligning to the interface and numerically show first-order convergence.

Localization and mapping are key capabilities for self-driving vehicles. In this paper, we build on Kimera and extend it to use multiple cameras as well as external (eg wheel) odometry sensors, to obtain accurate and robust odometry estimates in real-world problems. Additionally, we propose an effective scheme for closing loops that circumvents the drawbacks of common alternatives based on the Perspective-n-Point method and also works with a single monocular camera. Finally, we develop a method for dense 3D mapping of the free space that combines a segmentation network for free-space detection with a homography-based dense mapping technique. We test our system on photo-realistic simulations and on several real datasets collected on a car prototype developed by the Ford Motor Company, spanning both indoor and outdoor parking scenarios. Our multi-camera system is shown to outperform state-of-the art open-source visual-inertial-SLAM pipelines (Vins-Fusion, ORB-SLAM3), and exhibits an average trajectory error under 1% of the trajectory length across more than 8km of distance traveled (combined across all datasets). A video showcasing the system is available at: youtu.be/H8CpzDpXOI8.

Meshfree Lagrangian frameworks for free surface flow simulations do not conserve fluid volume. Meshfree particle methods like SPH are not mimetic, in the sense that discrete mass conservation does not imply discrete volume conservation. On the other hand, meshfree collocation methods typically do not use any notion of mass. As a result, they are neither mass conservative nor volume conservative at the discrete level. In this paper, we give an overview of various sources of conservation errors across different meshfree methods. The present work focuses on one specific issue: unreliable volume and mass definitions. We introduce the concept of representative masses and densities, which are essential for accurate post-processing especially in meshfree collocation methods. Using these, we introduce an artificial compression or expansion in the fluid to rectify errors in volume conservation. Numerical experiments show that the introduced frameworks significantly improve volume conservation behaviour, even for complex industrial test cases such as automotive water crossing.

We apply the Physics Informed Neural Network (PINN) to the problem of wildfire fire-front modelling. We use the PINN to solve the level-set equation, which is a partial differential equation that models a fire-front through the zero-level-set of a level-set function. The result is a PINN that simulates a fire-front as it propagates through the spatio-temporal domain. We show that popular optimisation cost functions used in the literature can result in PINNs that fail to maintain temporal continuity in modelled fire-fronts when there are extreme changes in exogenous forcing variables such as wind direction. We thus propose novel additions to the optimisation cost function that improves temporal continuity under these extreme changes. Furthermore, we develop an approach to perform data assimilation within the PINN such that the PINN predictions are drawn towards observations of the fire-front. Finally, we incorporate our novel approaches into a Bayesian PINN (B-PINN) to provide uncertainty quantification in the fire-front predictions. This is significant as the standard solver, the level-set method, does not naturally offer the capability for data assimilation and uncertainty quantification. Our results show that, with our novel approaches, the B-PINN can produce accurate predictions with high quality uncertainty quantification on real-world data., Comment: Accepted for publication in Spatial Statistics

Computational simulations of wildfire spread typically employ empirical rate-of-spread calculations under various conditions (such as terrain, fuel type, weather). Small perturbations in conditions can often lead to significant changes in fire spread (such as speed and direction), necessitating a computationally expensive large set of simulations to quantify uncertainty. Model emulation seeks alternative representations of physical models using machine learning, aiming to provide more efficient and/or simplified surrogate models. We propose a dedicated spatio-temporal neural network based framework for model emulation, able to capture the complex behaviour of fire spread models. The proposed approach can approximate forecasts at fine spatial and temporal resolutions that are often challenging for neural network based approaches. Furthermore, the proposed approach is robust even with small training sets, due to novel data augmentation methods. Empirical experiments show good agreement between simulated and emulated firefronts, with an average Jaccard score of 0.76.

The level-set method is a prominent approach to modelling the evolution of a fire over time based on a characterised rate of spread. It however does not provide a direct means for assimilating new data and quantifying uncertainty. Fire front predictions can be more accurate and agile if the models are able to assimilate data in real time. Furthermore, uncertainty estimation of the location and spread of the fire is critical for decision making. Using Bayesian filtering approaches, we extend the level-set method to allow for data assimilation and uncertainty quantification. We demonstrate these approaches on data from a controlled fire.

Data preprocessing is a crucial stage in the data analysis pipeline, with both technical and social aspects to consider. Yet, the attention it receives is often lacking in research practice and dissemination. We present the Smallset Timeline, a visualisation to help reflect on and communicate data preprocessing decisions. A "Smallset" is a small selection of rows from the original dataset containing instances of dataset alterations. The Timeline is comprised of Smallset snapshots representing different points in the preprocessing stage and captions to describe the alterations visualised at each point. Edits, additions, and deletions to the dataset are highlighted with colour. We develop the R software package, smallsets, that can create Smallset Timelines from R and Python data preprocessing scripts. Constructing the figure asks practitioners to reflect on and revise decisions as necessary, while sharing it aims to make the process accessible to a diverse range of audiences. We present two case studies to illustrate use of the Smallset Timeline for visualising preprocessing decisions. Case studies include software defect data and income survey benchmark data, in which preprocessing affects levels of data loss and group fairness in prediction tasks, respectively. We envision Smallset Timelines as a go-to data provenance tool, enabling better documentation and communication of preprocessing tasks at large., Comment: In 2022 ACM Conference on Fairness, Accountability, and Transparency (FAccT '22), June 21-24, 2022, Seoul, Republic of Korea

In this paper, we present a new model to simulate the formation, evolution, and break up of a thin film of fluid flowing over a curved surface. Referred to as the discrete droplet method (DDM), the model captures the evolution of thin fluid films by tracking individual moving fluid droplets. In contrast to existing thin film models that solve a PDE to determine the film height, here, we compute the film height by numerical integration based on the aggregation of droplets. The novelty of this approach in using droplets makes it suitable for simulating the formation of fluid films, and modelling thin film flows on partially wetted surfaces. The DDM is a Lagrangian approach, with a force balance on each droplet governing the motion, and derivatives approximated using a smoothed particle hydrodynamics (SPH) like approach. The proposed model is thoroughly validated by comparing results against analytical solutions, against the results of the shallow-water equations for thin film flow, and also against results from a full 3D resolved Navier Stokes model. We also present the use of the DDM on an industrial test case. The results highlight the effectiveness of the model for simulations of flows with thin films.

We present a meshfree generalized finite difference method for solving Poisson's equation with a diffusion coefficient that contains jump discontinuities up to several orders of magnitude. To discretize the diffusion operator, we formulate a strong form method that uses a smearing of the discontinuity; and a conservative formulation based on locally computed Voronoi cells. Additionally, we propose a novel conservative formulation for enforcing Neumann boundary conditions that is compatible with the conservative formulation of the diffusion operator. Finally, we introduce a way to switch from the strong form to the conservative formulation to obtain a locally conservative and positivity preserving scheme. The presented numerical methods are benchmarked against four test cases of varying complexity and jump magnitude on point clouds with nodes that are not aligned to the discontinuity. Our results show that the new hybrid method that switches between the two formulations produces better results than the classical generalized finite difference approach for high jumps in diffusivity.

Forecasting bushfire spread is an important element in fire prevention and response efforts. Empirical observations of bushfire spread can be used to estimate fire response under certain conditions. These observations form rate-of-spread models, which can be used to generate simulations. We use machine learning to drive the emulation approach for bushfires and show that emulation has the capacity to closely reproduce simulated fire-front data. We present a preliminary emulator approach with the capacity for fast emulation of complex simulations. Large numbers of predictions can then be generated as part of ensemble estimation techniques, which provide more robust and reliable forecasts of stochastic systems., Comment: Machine Learning and the Physical Sciences Workshop, NeurIPS, 2021

We introduce a meshfree collocation framework to model the phase change from liquid to vapor at or above the boiling point. While typical vaporization or boiling simulations focus on the vaporization from the bulk of the fluid, here we include the possibility of vaporization from the free surface, when a moving fluid comes into contact with a superheated surface. We present a continuum, one-fluid approach in which the liquid and vapor phases are modeled with the same constitutive equations, with different material properties. The novelty here is a monolithic approach without explicit modeling of the interface between the phases, neither in a sharp nor diffuse sense. Furthermore, no interface boundary conditions or source terms are needed between the liquid and vapor phases. Instead, the phase transition is modeled only using material properties varying with temperature. Towards this end, we also present an enrichment of strong form meshfree generalized finite difference methods (GFDM) to accurately capture derivatives in the presence of jumps in density, viscosity, and other physical properties. The numerical results show a good agreement with experimental results, and highlight the ability of our proposed framework to model phase changes with large jumps.

With the recent boost in autonomous driving, increased attention has been paid on radars as an input for occupancy mapping. Besides their many benefits, the inference of occupied space based on radar detections is notoriously difficult because of the data sparsity and the environment dependent noise (e.g. multipath reflections). Recently, deep learning-based inverse sensor models, from here on called deep ISMs, have been shown to improve over their geometric counterparts in retrieving occupancy information. Nevertheless, these methods perform a data-driven interpolation which has to be verified later on in the presence of measurements. In this work, we describe a novel approach to integrate deep ISMs together with geometric ISMs into the evidential occupancy mapping framework. Our method leverages both the capabilities of the data-driven approach to initialize cells not yet observable for the geometric model effectively enhancing the perception field and convergence speed, while at the same time use the precision of the geometric ISM to converge to sharp boundaries. We further define a lower limit on the deep ISM estimate's certainty together with analytical proofs of convergence which we use to distinguish cells that are solely allocated by the deep ISM from cells already verified using the geometric approach.

Experimental and field investigations for solution mining processes have improved intensely in recent years. Due to today's computing capacities, three-dimensional simulations of potential salt solution caverns can further enhance the understanding of these processes. They serve as a "virtual prototype" of a projected site and support planning in reasonable time. In this contribution, we present a meshfree Generalized Finite Difference Method (GFDM) based on a cloud of numerical points that is able to simulate solution mining processes on microscopic as well as macroscopic scales, which differ significantly in both the spatial and temporal scale. Focusing on anticipated industrial requirements, Lagrangian and Eulerian formulations including an Arbitrary Lagrangian-Eulerian (ALE) approach are considered.

We aim to model unknown file processing. As the content of log files often evolves over time, we established a dynamic statistical model which learns and adapts processing and parsing rules. First, we limit the amount of unstructured text by focusing only on those frequent patterns which lead to the desired output table similar to Vaarandi [10]. Second, we transform the found frequent patterns and the output stating the parsed table into a Hidden Markov Model (HMM). We use this HMM as a specific, however, flexible representation of a pattern for log file processing. With changes in the raw log file distorting learned patterns, we aim the model to adapt automatically in order to maintain high quality output. After training our model on one system type, applying the model and the resulting parsing rule to a different system with slightly different log file patterns, we achieve an accuracy over 99%.

In order to ensure trouble-free operation, prediction of hardware failures is essential. This applies especially to medical systems. Our goal is to determine hardware which needs to be exchanged before failing. In this work, we focus on predicting failures of 20-channel Head/Neck coils using image-related measurements. Thus, we aim to solve a classification problem with two classes, normal and broken coil. To solve this problem, we use data of two different levels. One level refers to one-dimensional features per individual coil channel on which we found a fully connected neural network to perform best. The other data level uses matrices which represent the overall coil condition and feeds a different neural network. We stack the predictions of those two networks and train a Random Forest classifier as the ensemble learner. Thus, combining insights of both trained models improves the prediction results and allows us to determine the coil's condition with an F-score of 94.14% and an accuracy of 99.09%.

Already before systems malfunction one has to know if hardware components will fail in near future in order to counteract in time. Thus, unplanned downtime is ought to be avoided. In medical imaging, maximizing the system's uptime is crucial for patients' health and healthcare provider's daily business. We aim to predict failures of Head/Neck coils used in Magnetic Resonance Imaging (MRI) by training a statistical model on sequential data collected over time. As image features depend on the coil's condition, their deviations from the normal range already hint to future failure. Thus, we used image features and their variation over time to predict coil damage. After comparison of different time series classification methods we found Long Short Term Memorys (LSTMs) to achieve the highest F-score of 86.43% and to tell with 98.33% accuracy if hardware should be replaced.

Valley-selective optical selection rules and a spin-valley locking in transition-metal dichalcogenide (TMDC) monolayers are at the heart of "valleytronic physics", which exploits the valley degree of freedom and has been a major research topic in recent years. In contrast, valleytronic properties of TMDC bilayers have not been in the focus so much by now. Here, we report on the valleytronic properties and optical characterization of bilayers of WS2 as a representative TMDC material. In particular, we study the influence of the relative layer alignment in TMDC homo-bilayer samples on their polarization-dependent optical properties. Therefore, CVD-grown WS2 bilayer samples have been prepared that favor either the inversion symmetric AA' stacking or AB stacking without inversion symmetry during synthesis. Subsequently, a detailed analysis of reflection contrast and photoluminescence spectra under different polarization conditions has been performed. We observe circular and linear dichroism of the photoluminescence that is more pronounced for the AB stacking configuration. Our experimental findings are supported by theoretical calculations showing that the observed dichroism can be linked to optical selection rules, that maintain the spin-valley locking in the AB-stacked WS2 bilayer, whereas a spin-layer-locking is present the inversion symmetric AA' bilayer instead. Furthermore, our theoretical calculations predict a small relative shift of the excitonic resonances in both stacking configurations, which is also experimentally observed.

To perform high speed tasks, sensors of autonomous cars have to provide as much information in as few time steps as possible. However, radars, one of the sensor modalities autonomous cars heavily rely on, often only provide sparse, noisy detections. These have to be accumulated over time to reach a high enough confidence about the static parts of the environment. For radars, the state is typically estimated by accumulating inverse detection models (IDMs). We employ the recently proposed evidential convolutional neural networks which, in contrast to IDMs, compute dense, spatially coherent inference of the environment state. Moreover, these networks are able to incorporate sensor noise in a principled way which we further extend to also incorporate model uncertainty. We present experimental results that show This makes it possible to obtain a denser environment perception in fewer time steps., Comment: Submitted for Intelligent Vehicle Symposium 2019

One essential step to realize modern driver assistance technology is the accurate knowledge about the location of static objects in the environment. In this work, we use artificial neural networks to predict the occupation state of a whole scene in an end-to-end manner. This stands in contrast to the traditional approach of accumulating each detection's influence on the occupancy state and allows to learn spatial priors which can be used to interpolate the environment's occupancy state. We show that these priors make our method suitable to predict dense occupancy estimations from sparse, highly uncertain inputs, as given by automotive radars, even for complex urban scenarios. Furthermore, we demonstrate that these estimations can be used for large-scale mapping applications., Comment: Submitted for Automotive Meets Electronics 2019

We propose a novel framework to solve PDEs on moving manifolds, where the evolving surface is represented by a moving point cloud. This has the advantage of avoiding the need to discretize the bulk volume around the surface, while also avoiding the need to have a global mesh. Distortions in the point cloud as a result of the movement are fixed by local adaptation. We first establish a comprehensive Lagrangian framework for arbitrary movement of curves and surfaces given by point clouds. Collision detection algorithms between point cloud surfaces are introduced, which also allow the handling of evolving manifolds with topological changes. We then couple this Lagrangian framework with a meshfree Generalized Finite Difference Method (GFDM) to approximate surface differential operators, which together give a method to solve PDEs on evolving manifolds. The applicability of this method is illustrated with a range of numerical examples, which include advection-diffusion equations with large deformations of the surface, curvature dependent geometric motion, and wave equations on evolving surfaces.

In this paper, we propose a novel meshfree Generalized Finite Difference Method (GFDM) approach to discretize PDEs defined on manifolds. Derivative approximations for the same are done directly on the tangent space, in a manner that mimics the procedure followed in volume-based meshfree GFDMs. As a result, the proposed method not only does not require a mesh, it also does not require an explicit reconstruction of the manifold. In contrast to existing methods, it avoids the complexities of dealing with a manifold metric, while also avoiding the need to solve a PDE in the embedding space. A major advantage of this method is that all developments in usual volume-based numerical methods can be directly ported over to surfaces using this framework. We propose discretizations of the surface gradient operator, the surface Laplacian and surface Diffusion operators. Possibilities to deal with anisotropic and discontinous surface properties (with large jumps) are also introduced, and a few practical applications are presented.

We study optical pumping of resident electron spins under resonant excitation of trions in n-type CdTe/(Cd,Mg)Te quantum wells subject to a transverse magnetic field. In contrast to the comprehensively used time-resolved pump-probe techniques with polarimetric detection, we exploit here a single beam configuration in which the time-integrated intensity of the excitation laser light transmitted through the quantum wells is detected. The transmitted intensity reflects the bleaching of light absorption due to optical pumping of the resident electron spins and can be used to evaluate the Larmor precession frequency of the optically oriented carriers and their spin relaxation time. Application of the magnetic field leads to depolarization of the electron spin ensemble so that the Hanle effect is observed. Excitation with a periodic sequence of laser pulses leads to optical pumping in the rotating frame if the Larmor precession frequency is synchronized with the pulse repetition rate. This is manifested by the appearance of Hanle curves every 3.36 or 44.2 mT for pulse repetition rates of 75.8 or 999 MHz, respectively. From the experimental data we evaluate the g factor of |g|=1.61 and the spin relaxation time of 14 ns for the optically pumped resident electrons, in agreement with previous time-resolved pump-probe studies., Comment: 6 pages, 3 figures

Lubiw showed that several variants of Graph Isomorphism are NP-complete, where the solutions are required to satisfy certain additional constraints [SICOMP 10, 1981]. One of these, called Isomorphism With Restrictions, is to decide for two given graphs $X_1=(V,E_1)$ and $X_2=(V,E_2)$ and a subset $R\subseteq V\times V$ of forbidden pairs whether there is an isomorphism $\pi$ from $X_1$ to $X_2$ such that $\pi(i)\neq j$ for all $(i,j)\in R$. We prove that this problem and several of its generalizations are in fact in FPT: - The problem of deciding whether there is an isomorphism between two graphs that moves k vertices and satisfies Lubiw-style constraints is in FPT, with k and the size of $R$ as parameters. The problem remains in FPT if a CNF of such constraints is allowed. It follows that the problem to decide whether there is an isomorphism that moves exactly k vertices is in FPT. This solves a question left open in our article on exact weight automorphisms [STACS 2017]. - When the weight and complexity are unrestricted, finding isomorphisms that satisfy a CNF of Lubiw-style constraints can be solved in FPT with access to a GI oracle. - Checking if there is an isomorphism $\pi$ between two graphs with complexity t is also in FPT with t as parameter, where the complexity of a permutation is the Cayley measure defined as the minimum number t such that $\pi$ can be expressed as a product of t transpositions. - We consider a more general problem in which the vertex set of a graph X is partitioned into Red and Blue, and we are interested in an automorphism that stabilizes Red and Blue and moves exactly k vertices in Blue, where k is the parameter. This problem was introduced by [Downey and Fellows 1999], and we showed [STACS 2017] that it is W[1]-hard even with color classes of size 4 inside Red. Now, for color classes of size at most 3 inside Red, we show the problem is in FPT., Comment: An extended abstract of this article appears in the proceedings of IPEC 2017

In Lagrangian meshfree methods, the underlying spatial discretization, referred to as a point cloud or a particle cloud, moves with the flow velocity. In this paper, we consider different numerical methods of performing this movement of points or particles. The movement is most commonly done by a first order method, which assumes the velocity to be constant within a time step. We show that this method is very inaccurate and that it introduces volume and mass conservation errors. We further propose new methods for the same which prescribe an additional ODE system that describes the characteristic velocity. Movement is then performed along this characteristic velocity. The first new way of moving points is an extension of mesh-based streamline tracing ideas to meshfree methods. In the second way, the movement is done based on the difference in approximated streamlines between two time levels, which approximates the pathlines in unsteady flow. Numerical comparisons show these method to be vastly superior to the conventionally used first order method.

Lack of conservation has been the biggest drawback in meshfree generalized finite difference methods (GFDMs). In this paper, we present a novel modification of classical meshfree GFDMs to include local balances which produce an approximate conservation of numerical fluxes. This numerical flux conservation is done within the usual moving least squares framework. Unlike Finite Volume Methods, it is based on locally defined control cells, rather than a globally defined mesh. We present the application of this method to an advection diffusion equation and the incompressible Navier - Stokes equations. Our simulations show that the introduction of flux conservation significantly reduces the errors in conservation in meshfree GFDMs., Comment: International Journal for Numerical Methods in Engineering

Meshfree solution schemes for the incompressible Navier--Stokes equations are usually based on algorithms commonly used in finite volume methods, such as projection methods, SIMPLE and PISO algorithms. However, drawbacks of these algorithms that are specific to meshfree methods have often been overlooked. In this paper, we study the drawbacks of conventionally used meshfree Generalized Finite Difference Method~(GFDM) schemes for Lagrangian incompressible Navier-Stokes equations, both operator splitting schemes and monolithic schemes. The major drawback of most of these schemes is inaccurate local approximations to the mass conservation condition. Further, we propose a new modification of a commonly used monolithic scheme that overcomes these problems and shows a better approximation for the velocity divergence condition. We then perform a numerical comparison which shows the new monolithic scheme to be more accurate than existing schemes.

There is increasing evidence for specific cortical and subcortical large-scale human epileptic networks to be involved in the generation, spread, and termination of not only primary generalized but also focal onset seizures. The complex dynamics of such networks has been studied with methods of analysis from graph theory. In addition to investigating network-specific characteristics, recent studies aim to determine the functional role of single nodes---such as the epileptic focus---in epileptic brain networks and their relationship to ictogenesis. Utilizing the concept of betweenness centrality to assess the importance of network nodes, previous studies reported the epileptic focus to be of highest importance prior to seizures, which would support the notion of a network hub that facilitates seizure activity. We performed a time-resolved analysis of various aspects of node importance in epileptic brain networks derived from long-term, multi-channel, intracranial electroencephalographic recordings from an epilepsy patient. Our preliminary findings indicate that the epileptic focus is not consistently the most important network node, but node importance may drastically vary over time.

Monolayers of transition-metal dichalcogenides such as WSe2 have become increasingly attractive due to their potential in electrical and optical applications. Because the properties of these 2D systems are known to be affected by their surroundings, we report how the choice of the substrate material affects the optical properties of monolayer WSe2. To accomplish this study, pump-density-dependent micro-photoluminescence measurements are performed with time-integrating and time-resolving acquisition techniques. Spectral information and power-dependent mode intensities are compared at 290K and 10K for exfoliated WSe2 on SiO2/Si, sapphire (Al2O3), hBN/Si3N4/Si, and MgF2, indicating substrate-dependent appearance and strength of exciton, trion, and biexciton modes. Additionally, one CVD-grown WSe2 monolayer on sapphire is included in this study for direct comparison with its exfoliated counterpart. Time-resolved micro-photoluminescence shows how radiative decay times strongly differ for different substrate materials. Our data indicates exciton-exciton annihilation as a shortening mechanism at room temperature, and subtle trends in the decay rates in correlation to the dielectric environment at cryogenic temperatures. On the measureable time scales, trends are also related to the extent of the respective 2D-excitonic modes' appearance. This result highlights the importance of further detailed characterization of exciton features in 2D materials, particularly with respect to the choice of substrate.

Layered transition-metal dichalcogenides have attracted great interest in the last few years. Thinned down to the monolayer limit they change from an indirect band structure to a direct band gap in the visible region. Due to the monolayer thickness the inversion symmetry of the crystal is broken and spin and valley are coupled to each other. The degeneracy between the two equivalent valleys, K and K', respectively, can be lifted by applying an external magnetic field. Here, we present photoluminescence measurements of CVD-grown tungsten disulphide (WS${_2}$) monolayers at temperatures of 2 K. By applying magnetic fields up to 7 T in Faraday geometry, a splitting of the photoluminescence peaks can be observed. The magnetic field dependence of the A-exciton, the trion and three bound exciton states is discussed and the corresponding g-factors are determined., Comment: 4 pages, 4 figures

In this paper we study the complexity of the following problems: Given a colored graph X=(V,E,c), compute a minimum cardinality set S of vertices such that no nontrivial automorphism of X fixes all vertices in S. A closely related problem is computing a minimum base S for a permutation group G on [n] given by generators, i.e., a minimum cardinality subset S of [n] such that no nontrivial permutation in G fixes all elements of S. Our focus is mainly on the parameterized complexity of these problems. We show that when k=|S| is treated as parameter, then both problems are MINI[1]-hard. For the dual problems, where k=n-|S| is the parameter, we give FPT algorithms. A notion closely related to fixing is called individualization. Individualization combined with the Weisfeiler-Leman procedure is a fundamental technique in algorithms for Graph Isomorphism. Motivated by the power of individualization, in the present paper we explore the complexity of individualization: what is the minimum number of vertices we need to individualize in a given graph such that color refinement "succeeds" on it. Here "succeeds" could have different interpretations, and we consider the following: It could mean the individualized graph becomes: (a) discrete, (b) amenable, (c) compact, or (d) refinable. In particular, we study the parameterized versions of these problems where the parameter is the number of vertices individualized. We show a dichotomy: For graphs with color classes of size at most 3 these problems can be solved in polynomial time (even in logspace), while starting from color class size 4 they become W[P]-hard., Comment: An abridged version of this article appears in the proceedings of MFCS 2016

The coronagraph instrument on the WFIRST-AFTA mission study has two coronagraphic architectures, shaped pupil and hybrid Lyot, which may be interchanged for use in different observing scenarios. Each architecture relies on newly-developed mask components to function in the presence of the AFTA aperture, and so both must be matured to a high technology readiness level (TRL) in advance of the mission. A series of milestones were set to track the development of the technologies required for the instrument; in this paper, we report on completion of WFIRST-AFTA Coronagraph Milestone 2---a narrowband $10^{-8}$ contrast test with static aberrations for the shaped pupil---and the plans for the upcoming broadband Coronagraph Milestone 5., Comment: 35 pages, 15 figures

The connection between the non-equilibrium dynamics of isolated quantum many-body systems and statistical mechanics is a fundamental open question. It is generally believed that the unitary quantum evolution of a sufficiently complex system leads to an apparent maximum-entropy state that can be described by thermodynamical ensembles. However, conventional ensembles fail to describe the large class of systems that exhibit non-trivial conserved quantities. Instead, generalized ensembles have been predicted to maximize entropy in these systems. In our experiments we explicitly show that a degenerate one-dimensional Bose gas relaxes to a state that can be described by such a generalized ensemble. This is verified through a detailed study of correlation functions up to 10th order. The applicability of the generalized ensemble description for isolated quantum many-body systems points to a natural emergence of classical statistical properties from the microscopic unitary quantum evolution., Comment: 5 pages + 4 pages supp. mat., 4 figures

The isomorphism problem is known to be efficiently solvable for interval graphs, while for the larger class of circular-arc graphs its complexity status stays open. We consider the intermediate class of intersection graphs for families of circular arcs that satisfy the Helly property. We solve the isomorphism problem for this class in logarithmic space. If an input graph has a Helly circular-arc model, our algorithm constructs it canonically, which means that the models constructed for isomorphic graphs are equal., Comment: 22 pages, 5 figures. Section 5 is revised in this version

A circular-arc hypergraph $H$ is a hypergraph admitting an arc ordering, that is, a circular ordering of the vertex set $V(H)$ such that every hyperedge is an arc of consecutive vertices. An arc ordering is tight if, for any two hyperedges $A$ and $B$ such that $A$ is a nonempty subset of $B$ and $B$ is not equal to $V(H)$, the corresponding arcs share a common endpoint. We give sufficient conditions for $H$ to have, up to reversing, a unique arc ordering and a unique tight arc ordering. These conditions are stated in terms of connectedness properties of $H$. It is known that $G$ is a proper circular-arc graph exactly when its closed neighborhood hypergraph $N[G]$ admits a tight arc ordering. We explore connectedness properties of $N[G]$ and prove that, if $G$ is a connected, twin-free, proper circular-arc graph with non-bipartite complement, then $N[G]$ has, up to reversing, a unique arc ordering. If the complement of $G$ is bipartite and connected, then $N[G]$ has, up to reversing, two tight arc orderings. As a corollary, we notice that in both of the two cases $G$ has an essentially unique intersection representation. The last result also follows from the work by Deng, Hell, and Huang based on a theory of local tournaments., Comment: 21 pages, 8 figures